Signal and Image Registration: Application to Decrypt Marine Biological Archives
Recalage de Signaux Et D'images: Application au Décryptage D'archives Biologiques Marines
OPEN ACCESS
A robust variational setting is proposed for 1D signal registration and applied to the computation of shape geodesics for shape classification issues. This approach is extended to be applied for matching images of shape sequences. This geometric approach is mainly addressed to poorly contrasted images where the intensity-based registration fails. For validation purposes, experiments are carried out on real signals and images issued from marine biological archives which depict a high interindividual variability such that registration-based approaches are of particular interest.
1D signal registration
Given two signals S(t) and S (t), the registration consists in retrieving the transformation that best matches points of similar characteristics. This transformation must be maintained smooth. Formally, the matching problem resorts to determining the transformation function φ(t) such that S(t) = S (φ(t)). This issue is stated as the minimization of an energy E(φ) of the form given in Eq. (1), involving a data-driven term, ED, that evaluates the similarity between S(t) and S(φ(t)) and a regularization term, ER. The choice of the similarity measure depends on the nature of the signals to be registered. Here, we consider signals of same nature such that ED (S,S (φ))is given by a norm S − S(φ). To improve the registration robustness with respect to the outlier data a robust norm is exploited: S − S(φ). The principle is supported by the use of a function that adjusts a weight ω by increasing its value to the data points with low variation compared to other points. Several forms of robust estimators ρ were proposed [1]. To solve for minimization E(φ) two methods are considered: a dynamic programming and iterative gradient-based method. As an application to biological archives, we propose to use 1D signal registration of a measured chemical signature from fish otolith and the records of water temperature in order to estimate the otolith growth law (Fig. 1).
Contour matching
The 1D signal registration approach is applied to the computation of shape geodesics and then to boundary-based shape classification issues. Shape analysis from geodesics in shape space has emerged as a powerful tool to develop geometrically invariant shape comparison methods. Geodesics in the shape space are defined as paths between two shapes with respect to some metric (Fig. 2). This metric is chosen to be invariant for a given set of transformations (e.g. rotation, scaling, translation,… ). Retrieving the geodesic path in shape space between any two closed contours resorts to a registration issue with respect to the considered metric. Given a curve parametrization of the shapes, it comes to the registration of two 1D signals (Fig. 3). Here, we exploit shape geodesics for boundary-based shape classification and propose to compare shapes on the basis of a metric that takes into consideration the matching of points of similar features (Eq. (9)-(11)). The proposed framework is applied to marine stock and species discrimination. The use of the geodesic approach provides always benefits to classification (Tab. 1), it significantly outperforms the Fourier scheme with a gain in term of correct classification rate over the three processed datasets.
Image registration
In biological science, there are images depicting shape sequences. For example, otolith images involve concentric rings referring to an accretionnary growth from the initial core to the otolith outline. These images are highly geometrically structured but flat in terms of contrast, such that gray level information is not sufficient itself to perform the registration. Here, we propose to register these images through the registration of the corresponding shape sequences (Fig. 5). In [2], we have developed a variational approach for 2D image-based reconstruction of such individual shape histories using a level-set representation (Fig. 7). Using the metric used for planar curves (Eq. (9)) in the term ED of our functional E(φ) , and integrating for all levels, the registration issue resorts to minimizing Eq. (15). To test the proposed framework, the experiments are first carried out on synthetic images illustrated in Fig. 10. In minimization with iterative scheme (Fig. 8 and Fig. 9), one can see that when the initialization is so far, a risk of convergence to a local minimum exists if we did not add the robust weights. Using dynamic programming, results are similar to those of the robust iterative scheme but the associated computational time is greater (more than 10 times greater). In Fig. 10, we can see that intensity-based registration does not correctly register these images. On the other hand, geometric registration is able to find the real transformation, both geometric and iconic errors are so negligible. Besides, we have tested the proposed algorithm on several real images of otoliths of different species and different age groups, we have had satisfactory results even with a small number of sampled levels (age + 2 including the contour) as illustrated in Fig. 5 and Fig. 11-13.
Résumé
Une approche variationnelle et robuste est proposée pour le recalage de signaux 1D et appliquée au calcul des géodésiques de formes pour la classification. L'approche est ensuite étendue au recalage d'images de séquences de formes. Cette approche de recalage basé-géométrie est plus adaptée aux images peu contrastées pour lesquelles le recalage basé-intensité trouve toutes ses limites. Une étude de validation est menée sur des signaux et des images issus d'archives biologiques marines, qui présentent une grande variabilité interindividuelle, où les approches de recalage sont d'un intérêt tout particulier.
Signal registration, image registration, geodesics in shape space, optimization, shape classification, fish otoliths.
Mots clés
Recalage de signaux, recalage d'images, géodésiques dans l'espace des formes, optimisation, classification de formes, otolithes de poissons.
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